The Sacred Timeline apparently isn't a single timeline, but rather a bundle of timelines all flowing in the same general direction. See this answer to another question for a more detailed explanation, with relevant citations.
As for the main thrust of your question, I take the view that there's no fundamental difference between the "timelines" mentioned in the MCU, and parallel universes. There are a number of things that point to this being the case.
Firstly, within the Loki series, the "multiversal war" was presented as a war between different "timelines," and the existence of the multiverse itself linked to the branching of one timeline from another.
MISS MINUTES: Long ago, there was a vast multiversal war. Countless unique timelines battled each other for supremacy, nearly resulting in the total destruction of... well, everything. But then, the all-knowing Time-Keepers emerged, bringing peace by reorganizing the multiverse into a single timeline, the Sacred Timeline. Now, the Time-Keepers protect and preserve the proper flow of time for everyone and everything. But sometimes, people like you veer off the path the Time-Keepers created. We call those Variants. Maybe you started an uprising, or were just late for work. Whatever it was, stepping off your path created a nexus event, which, left unchecked, could branch off into madness, leading to another multiversal war.
Loki - S01E01 - "Glorious Purpose"
He Who Remains also stated that each of his variants lived in different "universes" stacked on top of one another, and used the words "universes" and "realities" interchangeably.
HE WHO REMAINS: Eons ago, before the TVA, a variant of myself lived on Earth in the 31st century. He was a scientist and he discovered that there were universes stacked on top of his own. At the same time, other versions of us were learning the same thing. Naturally, they made contact. And for a while, there was peace. Narcissistic, self-congratulatory peace. "I love your shoes." "I love your hair." "Oh, man, nice nose." "Thanks, man." Et cetera. They shared technology and knowledge. Using the best of their universes to improve the others. However... not every version of me was so... so pure of heart. To some of us, new worlds meant only one thing, new lands to be conquered. The peace between realities... erupted into all-out war, each variant fighting to preserve their universe and annihilate the others. This was almost the end... ladies and gentlemen, of everything and everyone.
SYLVIE: And then the Time-Keepers came along and saved us all.
HE WHO REMAINS: Amen. No. No. Nope, this is where we diverge from the dogma. That first variant encountered a creature created from all the tears in reality, capable of consuming time and space itself. A creature... you both know.
LOKI: Alioth.
HE WHO REMAINS: Bingo! I harnessed the beast's power and began experimenting on it. I weaponized Alioth and I ended... I ended the Multiversal War. Once I isolated our timeline, all I had to do was manage the flow of time and prevent any further branches. Hence, the TVA. Hence, the Time-Keepers and a highly efficient bureaucracy. Hence, ages... and ages of cosmic harmony. Hence... you're welcome.
Loki - S01E06 - "For All Time. Always."
Secondly, in Avengers: Endgame, the Ancient One used the word "realities" when distinguishing between different timelines, and Banner used the words "timeline" and "reality" interchangeably.
THE ANCIENT ONE: I'm sorry, I can't help you, Bruce. If I give up the Time Stone to help your Reality, I'm dooming my own.
BRUCE BANNER: With all due respect, I'm not sure the science really supports that.
THE ANCIENT ONE: The Infinity Stones create what you experience as the flow of time. Remove one stone and that flow splits. Now, this may benefit your reality, but my new one... not so much. In this new branched Reality, without our chief weapon against the forces of darkness, our world will be overrun. Millions will suffer. So, tell me, Doctor, can your science prevent all that?
BRUCE BANNER: No, but we can erase it. Because once we are done with the stones, we can return each one to its own timeline at the moment it was taken. So, chronologically, in that reality, it never left.
Avengers: Endgame
Thirdly, in an interview with ScreenCrush, the head writer of the Loki series, Michael Waldron, used the words "universes" and "timelines" interchangeably.
SCREENCRUSH: Okay, understood. So my question is if there is the one “Sacred Timeline” of the Marvel Universe that the TVA has been protecting for some significant stretch of time, then how can there also be so many alternate timelines and variants as well?
MICHAEL WALDRON: Okay, The best I can explain it is our approach with time travel was the philosophy basically that time is always happening. So there are infinite instances of time always occurring at once. So you and I are having this conversation right now. There’s another instance of us having this conversation 10 seconds ago. There’s another instance of time of us having this conversation 10 seconds in the future. Generally, those three instances — you could literally say they’re all different universes in a way different timelines — are all the same. There are minute little fluctuations in each instance of time. So in you and I’s conversation, five times out of ten, I pick up and I say, “Hello.” And four times out of ten, I say, “Hey, nice to meet you.” And then maybe one time out of ten, I’d say, “Hey man, f— you. I don’t want to do this interview.”
Creator Michael Waldron Answers All Our Questions About ‘Loki’ And ‘Heels’
Fourthly, in the first episode of the What If...? series, the Watcher stated that Peggy Carter's decision to stay in the room where Steve Rogers was supposed to be injected with Dr. Erskine's serum -- rather than head up to the booth, like she did in Captain America: The First Avenger -- created a new "universe."
THE WATCHER: Time. Space. Reality. It's more than a linear path. It's a prism of endless possibility, where a single choice can branch out into infinite realities, creating alternate worlds from the ones you know. I am the Watcher. I am your guide through these vast new realities. Follow me and ponder the question... "What if...?"
THE WATCHER: Earth, June, 1943. The Nazi army marches across Europe, leaving death and destruction. The Allied armies band together to create a new kind of soldier. A Super Soldier. At humanity's darkest hour, a skinny kid from Brooklyn became Captain America. After turning the tide of World War II, he made the ultimate sacrifice, restoring peace and saving this universe. But in another universe, a single choice created a whole new hero.
STEVE ROGERS: All this to make one Super Soldier.
PEGGY CARTER: Paris has fallen. London might be next. If this works, you could end the war. We mere mortals can only dream of doing such things.
DR. ABRAHAM ERSKINE: Agent Carter, wouldn't you be more comfortable in the booth?
PEGGY CARTER: No, I'd prefer to stay.
THE WATCHER: There. That's the moment that created a new universe. When asked to leave the room, Margaret "Peggy" Carter chose to stay. But soon it would be her venturing into the unknown and creating a new world.
What If...? - S01E01 - "What If... Captain Carter Were The First Avenger?"
I believe there is an important distinction to be made between the terms "timeline" and "universe" when discussing certain other franchises, such as Back to the Future. In that story, there are multiple versions of the timeline, but as far as we're shown, these versions don't exist simultaneously in parallel. Rather, there's only ever a single timeline and universe, the history of which is rewritten each time a change is made in the past.
Within the MCU though, where multiple timelines can clearly exist simultaneously in parallel -- each with their own version of Earth and other planets and stars -- the distinction between a "timeline" and a "universe" ceases to hold any practical significance that I can see.
